The present invention relates to a fθ lens in a laser scanning unit (LSU) and method of making the same, and more particularly to a fθ lens having multi-sections optical surface, instead of the prior-art which having single section optical surface with single coefficient set, in order to achieve higher tolerance in assembling quality and higher performance in scanning effects.
Commonly used technologies, applied in Laser Beam Printers are known and described in U.S. Pat. No. 5,128,795, U.S. Pat. No. 5,162,938, U.S. Pat. No. 5,329,399, U.S. Pat. No. 5,710,654, U.S Pat. No. 5,757,533, U.S. Pat. No. 5,619,362, U.S. Pat. No. 5,721,631, U.S. Pat. No. 5,553,729, U.S. Pat. No. 5,111,219, U.S. Pat. No. 5,995,131 and Japanese Patents 4-50908, 5-45580 etc. In all these Laser Scanning Units, the most favored way is to use a highly circumvolving (40000/min) polygonal mirror, to control the scanning of the Laser Beam.
A conventional LSU 1 will not be described with reference to FIGS. 1, 1A, and 1B to explain the structure and optic path in general LSU. As can be seen from FIG. 1, the LSU 1 includes a semiconductor laser 10 that serves as a light source to emit laser beams, which sequentially pass through an aperture 11 and a collimator 12. The laser beams pass through the collimator 12 to form parallel beams and then pass through a cylindrical lens 13, a main function of which is to cause a width of the parallel beams in a sub-major scanning direction or Y-axis to focus in a direction parallel to a major scanning direction or X-axis and thereby form a line image, which is a point in FIG. 1B. The LSU 1 also includes a polygonal mirror 14 that is adapted to rotate at high speed, so that a plurality of reflection mirror 15 uniformly and continuously arranged on the polygonal mirror 14 are just located at or in the vicinity of a focal point of the above-mentioned line image. The polygonal mirror 14 serves to control a direction in which the laser beams are projected from. The a plurality of continuous reflection mirrors 15 at high rotating speed are adapted to deflect and reflect laser beams incident on the reflection mirrors 15 in a direction parallel to the major scanning direction or X-axis to an f.theta. lens 16 at uniform angular velocity. The f.theta. lens 16 is located at one side of the polygonal mirror 14 and may be a single-element scanning lens, as shown in FIG. 1, or a two-element scanning lens, as that shown in the figures of U.S. Pat. No. 5,995,131. Laser beams incident on the f.theta. lens 16 via the reflection mirrors 15 on the polygonal mirror 14 are focused to form a circular light spot that is then projected onto a photoreceptor drum 17 to achieve a required scanning linearity. From the above, we know that the f.theta. lens 16 in LSU 1, with its structure illustrated by FIG. 2, the design of its optical surface is composed of the several equations and coefficient sets as follows:
1. Anamorphic Surface
  Z  =                              (          Cx          )                ⁢                  x          2                    +                        (          Cy          )                ⁢                  y          2                                                          1            +                                          (                                  1                  -                                                            (                                              1                        +                        Kx                                            )                                        ⁢                                                                  (                        Cx                        )                                            2                                        ⁢                                          x                      2                                                        -                                                            (                                              1                        +                        Ky                                            )                                        ⁢                                                                  (                        Cy                        )                                            2                                        ⁢                                          y                      2                                                                      )                                            1                /                2                                      +                                                                                          AR                ⁡                                  (                                                                                    (                                                  1                          -                          AP                                                )                                            ⁢                                              x                        2                                                              +                                                                  (                                                  1                          +                          AP                                                )                                            ⁢                                              y                        2                                                                              )                                            2                        +                                                                          BR              ⁢                                                (                                                                                    (                                                  1                          -                          BP                                                )                                            ⁢                                              x                        2                                                              +                                                                  (                                                  1                          +                          BP                                                )                                            ⁢                                              y                        2                                                                              )                                3                                      +                                                                                          CR                ⁡                                  (                                                                                    (                                                  1                          -                          CP                                                )                                            ⁢                                              x                        2                                                              +                                                                  (                                                  1                          +                          CP                                                )                                            ⁢                                              y                        2                                                                              )                                            4                        +                                                                          DR              ⁡                              (                                                                            (                                              1                        -                        DP                                            )                                        ⁢                                          x                      2                                                        +                                                            (                                              1                        +                        DP                                            )                                        ⁢                                          y                      2                                                                      )                                      5                              2. First Type Toric Surface:
      Z    =        ⁢          F      +                        G          *                      y            2                                    1          +                                    1              -                                                G                  2                                *                                  y                  2                                                                                    F      =      ⁠      ⁢                                    Cx            *                          x              2                                            1            +                                          1                -                                                      (                                          1                      +                      Kx                                        )                                    *                                      Cx                    2                                    *                                      x                    2                                                                                      +                                  ⁢                          ⁢                  A          ⁢                                          ⁢          4          *                      x            4                          +                  A          ⁢                                          ⁢          6          *                      x            6                          +                  A          ⁢                                          ⁢          8          *                      x            8                          +                  A          ⁢                                          ⁢          10          *                      x            10                                ;              G      =            ⁢              Cy                  1          -                      Cy            *            F                                ;  3. Second Type Toric Surface:
                                                                                             Z                  =                                    ⁢                                                                                                              x                          2                                                /                        R                                                                    1                        +                                                                              1                            -                                                                                          (                                                                  1                                  +                                  K                                                                )                                                            *                                                                                                (                                                                      x                                    /                                    R                                                                    )                                                                2                                                                                                                                                                          +                                                                                                                                          ⁢                                                            B                      ⁢                                                                                          ⁢                      2                      *                                              x                        2                                                              +                                          B                      ⁢                                                                                          ⁢                      4                      *                                              x                        4                                                              +                                          B                      ⁢                                                                                          ⁢                      6                      *                                              x                        6                                                              +                                          B                      ⁢                                                                                          ⁢                      8                      *                                              x                        8                                                              +                                          B                      ⁢                                                                                          ⁢                      10                      *                                              x                        10                                                                                                                                                                                r              ′                        =                        ⁢                          r              ⁡                              (                                  1                  +                                      D                    ⁢                                                                                  ⁢                    2                    *                                          x                      2                                                        +                                      D                    ⁢                                                                                  ⁢                    4                    *                                          x                      4                                                        +                                      D                    ⁢                                                                                  ⁢                    6                    *                                          x                      6                                                        +                                      D                    ⁢                                                                                  ⁢                    8                    *                                          x                      8                                                        +                                      D                    ⁢                                                                                  ⁢                    10                    *                                          x                      10                                                                      )                                                          ❘       
From the equations and coefficient sets mentioned above, we can know that the optical surfaces 21 and 22 of the conventional single fθ lens 2 are composed of one coefficient set, that is to say, the first optical surface 21 and the second optical surface 22 of the fθ lens are consisting of one single coefficient set separately. This design can make the two optical surfaces form a continuing surface profile, but there are problems existing as following:
(1). The main function of the fθ lens is to focus the input laser beams to a circular light spot, and then put the light spot onto a photoreceptor drum through scanning linearity. The diameter of the circular light spot on the scanning linearity is preferred to be 30 μm, or at least the spot should be within a circle whose diameter is 100 μm. As to the structure of a conventional LSU, with reference to FIG. 1, the laser beams pass to the reflection mirror 15 of polygon mirror 14, then reflected to fθ lens. Obviously, the central axis of the laser beams doesn't aim at the rotating axis of and the polygon mirror 14. Therefore, while designing fθ lens, we should take into consideration the above-mentioned deviation, which cause the optical surface of the best fθ lens to be with unsymmetrical characteristics .
(2). The difficulty in designing a fθ lens is greatly increased as there is unsymmetrical optical field on the optical surface of fθ lens while it should also acquire scanning linearity at the same time. As we all know, if the optical surface on the general fθ lens is designed with a single coefficient set, some trade-off and equilibrating amendment must take place for the two unsymmetrical optical field of fθ lens. However, all these not only raise problems for designing, but also lower the efficiency of the two unsymmetrical optical fields, because the single coefficient set could not reach the optical surfaces requests of the two unsymmetrical optical fields after trade-off amendment. As shown in FIG. 3, in this optical simulation, the fθ lens 2 is made of one coefficient set, and there are polygon mirror 23 polygon reflection mirror 24, laser beam 25 and the photoreceptor drum 26. We found that the light spot 27, within a certain distance, present different shapes rather than a circular light spot. Besides, the light spot sometimes departs from the center of the 100 μm circle, some of the light spots even reach out of the 100 μm circle. The results show that the optical efficiency is decreased by designing fθ lens with single coefficient set even after Trade-off, at the same time tolerance in assembling quality is also lowered and the difficulty in assembling is increased, too. It is the most pitted in designing the structure of fθ lens.